The agent-based and generic knowledge base

In order to describe cognitive synonymy or likeness of cognitive role, we need the concepts of agent-based knowledge and general knowledge. We describe these concepts here.

The agent-based knowledge base. When we grow up we learn, and we keep this knowledge in a knowledge base. For example, we learn (empirical) facts – like that fire is hot or what the name of our family members are – and we store these facts in our knowledge base. Moreover, we also learn general rules (that allow exceptions) and keep them in our knowledge base, too. A simple (notorious) instance of such a rule is: “If it is raining, the street is wet”. Of course, there might be situations where this rule doesn’t apply (e.g., if there is a roof above the street), but in general – that is, if we don’t have any reason to believe that something weird is going – we rely on this rule. Such rules are often called defeasible (since they can be “defeated” by exceptions). Thus, we can think of the knowledge base of an agent as a collection of facts and defeasible rules that can be updated: via learning we can add new facts and rules.58

Note that our knowledge base is closely connected to our beliefs: based on our knowledge base we form our beliefs. Roughly, in a given context (of everyday life) we believe thatϕ, if the following holds: After consulting both the facts we observed about the context we’re in and the relevant facts and rules in our knowledge base, we conclude – based on these rules – thatϕshould be the case.59

Also note that cognitive synonymy should be grounded in the rules in our knowl- edge base. For, we don’t first learn that two sentences are synonymous and then conclude that by believing one we also believe the other. Rather, we notice that the 57_{Note that we can take two sentences to refer to the same intension in a given context even though}

we know that, strictly speaking, they differ in intension. This is because of the same reason why likeness in cognitive role is not strictly hyperintensional: In most contexts, we take the two sentences about Bob’s beard to refer to the same intension (because such contexts don’t draw attention to the exact color of Bob’s beard), though we know that there are worlds that can distinguish the two sentences.

58_{The dynamics of a knowledge base are far more complex: We can also delete items and perform}

many more operations that are dealt with in the theory of belief revision. But here we, fortunately, don’t need more details about the dynamics of knowledge bases.

59_{Of course, not everything we believe is true: Mistakes can occur, for example, if we don’t realize that}

rules we gathered in our knowledge base tell us that whenever we come to believe one sentence we will also believe the other.

The generic knowledge base. We not only have to compute our own beliefs but also those of others. For many social interactions we need a so-calledtheory of mind: the ability to correctly ascribe mental states (like believing, intending, desiring, knowing, pretending) not only to ourselves but also – potentially different ones – to others. Now, to compute our beliefs it is enough to only consider our knowledge base and the facts and rules we observe about the context. But to compute the beliefs (and other mental states) of others we additionally have to consider boththeirknowledge bases and the facts and rules about the context thattheyobserve. However, their knowledge base is not directly accessible to us: we don’t know exactly what others take for granted. To still be able to ascribe beliefs to others, we need to assume that their knowledge base at least contains some “common knowledge” rules and facts that we share with them. To illustrate this, let’s consider a simple example:

In Alice’s village, they recently moved the local museum but they forgot to change the signs leading to it. Alice sees a touristy old man coming along, looking for the museum sign, finding it, and then moving on. She is deliberating whether she should tell him that the museum has moved, so she is wondering: Does he believe that the museum moved? Of course, Alice concludes that he doesn’t believe so, based on the following reasoning: The tourist also has in his knowledge base the commonly shared rule “If there is a sign to a museum, the museum will be there” (this is part of the “common knowledge” mentioned above). And he also saw the sign to the museum (this is a fact about the context that Alice saw the tourist observing). As Alice cannot see any reason why he would have inhibited that rule (the signs are not rusty, etc.), Alice reasons that the tourist must have concluded that the museum is where the signs lead to and not anywhere else. So Alice concludes that the tourist doesn’t believe that the museum moved.60

So we need to assume that there are some facts and rules that are present in every knowledge base of agents to which we want to ascribe a theory of mind. We call these facts and rules thegeneric knowledge base, and the set of relevant agentsA.

In fact, the need for a theory of mind is only one reason – an “agent-based” reason – for assuming a general knowledge base and a set of relevant agentsA. There also is the following second, “modeler-level” reason. We want to find out when two sentences have the same cognitive role and what laws govern this notion. However, having the same cognitive role is relative to an agent, but of course the laws governing it should be general: We’re not interested in how one particular agent individuates her cognitive content and take this to be the laws. Rather, we want to know what laws hold universally over all relevant possible agents.61 _{Once this setAof relevant}

60_{Once we’ve introduced negation as failure in the next section, we could better explain this way of}

handling negation (concluding that something is not the case if there is no information that it is the case). However, here this is not necessary because this is not the point of the example. The example should just illustrate how we compute the belief of others and that this requires a shared knowledge base.

61_{The situation is analogous to laws of nature: Not every fact about our world is a law of nature, rather}

possible agents is given, the generic knowledge base can be seen as the common ground of all the knowledge bases of the agents inA.

In the appendix (sectionA), we further discuss the notion of a set of relevant agents and a generic knowledge base. But for our purposes, the idea of these concepts should be clear enough.